Question

Unpolarized light with intensity I0 is incident on an ideal polarizing filter. The emerging light strikes a second ideal polarizing filter whose axis is at 42.0 ∘ to that of the first. Determine the intensity of the beam after it has passed through the second polarizer.

Answer 1

Answer:

$0.276I_0$

Explanation:

When unpolarized light passes through a polarizer, only the component of the light vibrating in the direction parallel to the axis of the polarizer passes through: therefore, the intensity of light is reduced by half, since only 1 out of 2 components passes through.

So, after the first polarizer, the intensity of light passing through is:

$I_1=\frac{I_0}{2}$

Where $I_0$ is the initial intensity of the unpolarized light.

Then, the light (which is now polarized) passes through the second polarizer. Here, the intensity of the light passing through the second polarizer is given by Malus Law:

$I_2=I_1 cos^2 \theta$

where:

$\theta$ is the angle between the axes of the two polarizers

In this problem the angle is

$\theta=42^{\circ}$

So the intensity after of light the 2nd polarizer is:

$I_2=I_1 (cos 42^{\circ})^2=\frac{I_0}{2}(cos 42^{\circ})^2=0.276I_0$